The Blues signed Michel from Sporting Gijon and Craig Gardner from Aston Villa in the January transfer window.
McLeish will be backed by the finances of new owner Carson Yeung.
Dunford said: “I expect it to be quite a busy summer. We will gear ourselves up for what I’m sure will be significant transfer movement in the summer.
“There are also eight or nine players likely to be leaving the club which means from a numerical point of view, we need new players of quality to supplement the ones we have got as well.”
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?